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C5×C22⋊#1043 #14522794

order2000
isoclinismisoclinic class of #87856
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×C22⋊#1043
unambiguous semidirect productC22⋊(C5×#1043)

Splittings

FittingC22×C53 ⋊ C4
SylowC53 ⋊ C22⋊C4

Subgroups

subgroupG/H
centerC2×C5C2×#1043
commutatorC2×C52C2×C4×C5
FrattiniC2C2×C5×#1043
FittingC22×C53C4
socleC2×C53C2×C4
prime radicalC22×C5×C5⋊D5C2
cosocleC2×C5⋊D5C22×C5
hypercenterC22×C5#1043
hypocenterC52C5×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C5 ◁ C22×C5

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 757);